ADAPTIVE CONTROL BASED ON THE APPLICATION OF A SIMPLIFIED UNIFORM STRUCTURES AND LEARNING PROCEDURES

The present state of creating a new branch of Soft Computing (SC) for particular problem classes, possibly wider than the control of mechanical systems, is reported in this article. Like "traditional" SC il evades the development of analytical system models, and uses uniform structures, but these structures originate from various Lie groups. The advantages are a drastic reduction in size and an increase in lucidity. The generally "stochastic or semistochastic" "learning" or parameter tuning seems to be replaceable by simple explicit algebraic procedures of limited steps, too. The idea originated from mechanical systems\u27 control while considering their general internal symmetry group, and later it was further developed by using specific general features of it on a much wider scale. Convergence considerations are given for MIMO and SISO systems, too. Simulation examples are presented for the control of the inverted pendulum with the use of the Generalized Lorentzian Matrices. It is concluded that the me/hod is promising and probably imposes acceptable convergence requirements in many cases

A two-layer approach to the coupled coherent states method

In this paper a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest (MCE) method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, MP/SOFT and CI expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations

Numerical Implementation and Test of the Modified Variational Multiconfigurational Gaussian Method for High-Dimensional Quantum Dynamics

In this paper, a new numerical implementation and a test of the modified variational multiconfigurational Gaussian (vMCG) equations are presented. In vMCG, the wave function is represented as a superposition of trajectory guided Gaussian coherent states, and the time derivatives of the wave function parameters are found from a system of linear equations, which in turn follows from the variational principle applied simultaneously to all wave function parameters. In the original formulation of vMCG, the corresponding matrix was not well-behaved and needed regularization, which required matrix inversion. The new implementation of the modified vMCG equations seems to have improved the method, which now enables straightforward solution of the linear system without matrix inversion, thus achieving greater efficiency, stability and robustness. Here the new version of the vMCG approach is tested against a number of benchmarks, which previously have been studied by split-operator, multiconfigurational time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH) techniques. The accuracy and efficiency of the new implementation of vMCG is directly compared with the method of coupled coherent states (CCS), another technique that uses trajectory guided grids. More generally we demonstrate that trajectory guided Gaussian based methods are capable of simulating quantum systems with tens or even hundreds of degrees of freedom previously accessible only for MCTDH and ML-MCTDH